Heaven, who held the second-round lead, also closed with a 70 to finish alone in second place. Peter Senior fired a closing round 5-under 65 to move into a share of third place at 6-under-par 274. He was joined there by David Smail, who closed with a 4-under 66.
Price, who entered the final day with a one-shot lead over Heaven and Chris Downes, struggled out of the gate with bogeys on Nos. 3 and 7, a pair of par-4s.
He settled down to birdie the ninth at The Grange Golf Club, and climbed back to even-par for his round with a birdie at the par-4 13th.
Success was short lived though as he faltered to his third and final bogey of the day at the par-3 15th. Price rebounded to birdie the 16th and return to 9 under. He closed with two pars to hang on for the win.
Heaven birdied the third before back-to-back bogeys from the fourth. The amateur bounced right back to birdie the sixth. He later birdied No. 10, but again stumbled to consecutive bogeys from the 14th.
He again came back to birdie the 16th. His birdie that could have forced a playoff at the last stopped just short of the hole and the title was Price's.
David Bransdon and Andrew Buckle shared fifth place at 5-under-par 275. Downes struggled to a 4-over 74 to fall into a tie for seventh place at 4-under-par 276. He was joined there by Adrian Percey, Wade Ormsby and Richard Best.